Not all those who book will turn up and Bodily and Weatherford (1995), using decision trees, show that the form of the solution remains unchanged 

 

  

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Quantitative Aspects Reverse an additional discount customer if p> Not all those who book will actually turn up and Bodily and Weatherford (1995), using decision trees, show that the form of the solution remains unchanged. A simpler approach for deciding how many discounts to offer is given in Weatherford and Bodily (1992). Another discounted unit is offered provided that the probability of overbooking, Pr(ob) (i.e. the probability that discounted demand plus full price demand will exceed capacity), is greater than the ratio of reduced price contribution Ra to the full price contribution R,, i.e. Allow discount if Pr(ob)> R₂ - Ra R₂ R₁ R₁ Thus the closer the discounted price is to the full price the more qd, (the quantity discounted) approaches the capacity of the facility C. In the approaches outlined above it was assumed that there was no correlation between the demand for full and discounted price accommodation. This is most unlikely in practice. Brumelle et al. (1990) attempt to overcome this problem by advancing a rule for situations where there is a positive correlation between the number of discounted customers (ga) and the number of full price paying customers (q,) and where discounts are issued first and there is no overlap in the time period during which discounts and full price are offered. Their rule is: 9d = max(0 sqs C:Pr[q> C-qiqazq]<P/P where C is the capacity Quantitative Aspects Reverse an additional discount customer if p> Not all those who book will actually turn up and Bodily and Weatherford (1995), using decision trees, show that the form of the solution remains unchanged. A simpler approach for deciding how many discounts to offer is given in Weatherford and Bodily (1992). Another discounted unit is offered provided that the probability of overbooking, Pr(ob) (i.e. the probability that discounted demand plus full price demand will exceed capacity), is greater than the ratio of reduced price contribution Ra to the full price contribution R,, i.e. Allow discount if Pr(ob)> R₂ - Ra R₂ R₁ R₁ Thus the closer the discounted price is to the full price the more qd, (the quantity discounted) approaches the capacity of the facility C. In the approaches outlined above it was assumed that there was no correlation between the demand for full and discounted price accommodation. This is most unlikely in practice. Brumelle et al. (1990) attempt to overcome this problem by advancing a rule for situations where there is a positive correlation between the number of discounted customers (ga) and the number of full price paying customers (q,) and where discounts are issued first and there is no overlap in the time period during which discounts and full price are offered. Their rule is: 9d = max(0 sqs C:Pr[q> C-qiqazq]<P/P where C is the capacity Quantitative Aspects Reverse an additional discount customer if p> Not all those who book will actually turn up and Bodily and Weatherford (1995), using decision trees, show that the form of the solution remains unchanged. A simpler approach for deciding how many discounts to offer is given in Weatherford and Bodily (1992). Another discounted unit is offered provided that the probability of overbooking, Pr(ob) (i.e. the probability that discounted demand plus full price demand will exceed capacity), is greater than the ratio of reduced price contribution Ra to the full price contribution R,, i.e. Allow discount if Pr(ob)> R₂ - Ra R₂ R₁ R₁ Thus the closer the discounted price is to the full price the more qd, (the quantity discounted) approaches the capacity of the facility C. In the approaches outlined above it was assumed that there was no correlation between the demand for full and discounted price accommodation. This is most unlikely in practice. Brumelle et al. (1990) attempt to overcome this problem by advancing a rule for situations where there is a positive correlation between the number of discounted customers (ga) and the number of full price paying customers (q,) and where discounts are issued first and there is no overlap in the time period during which discounts and full price are offered. Their rule is: 9d = max(0 sqs C:Pr[q> C-qiqazq]<P/P where C is the capacity Quantitative Aspects Reverse an additional discount customer if p> Not all those who book will actually turn up and Bodily and Weatherford (1995), using decision trees, show that the form of the solution remains unchanged. A simpler approach for deciding how many discounts to offer is given in Weatherford and Bodily (1992). Another discounted unit is offered provided that the probability of overbooking, Pr(ob) (i.e. the probability that discounted demand plus full price demand will exceed capacity), is greater than the ratio of reduced price contribution Ra to the full price contribution R,, i.e. Allow discount if Pr(ob)> R₂ - Ra R₂ R₁ R₁ Thus the closer the discounted price is to the full price the more qd, (the quantity discounted) approaches the capacity of the facility C. In the approaches outlined above it was assumed that there was no correlation between the demand for full and discounted price accommodation. This is most unlikely in practice. Brumelle et al. (1990) attempt to overcome this problem by advancing a rule for situations where there is a positive correlation between the number of discounted customers (ga) and the number of full price paying customers (q,) and where discounts are issued first and there is no overlap in the time period during which discounts and full price are offered. Their rule is: 9d = max(0 sqs C:Pr[q> C-qiqazq]<P/P where C is the capacity

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